Revision notes · Energy
Energy changes in a system, and the ways energy is stored before and after such changes
Energy stores and systems4.1.1.1
Definition: A system is an object, or a group of objects, that you are interested in. When a system changes, the way energy is stored changes too.
Energy can be stored as: kinetic (moving objects), thermal (temperature of an object), chemical (fuels, food, batteries), gravitational potential (objects raised above ground level), elastic potential (stretched or squashed springs), electrostatic (charges near each other), magnetic (magnets/coils near each other), and nuclear (the nucleus of atoms).
- •Ball rolling and hitting a wall: the system is the moving ball. When it hits the wall, some of its kinetic energy store is transferred to the surroundings as sound (and some to heating the ball and wall).
- •Vehicle braking to a stop: the system is the moving vehicle. Kinetic energy is transferred to the thermal energy stores of the brakes and surroundings, due to friction between the brakes and wheels.
🧠 Remember: Describe a system change as: name the store(s) energy starts in, name the store(s) it ends in, and say what caused the transfer (e.g. friction, a chemical reaction).
Changes in energy4.1.1.2
Definition: The kinetic energy store of a moving object depends on its mass and speed; the gravitational potential energy store of an object depends on its mass, height and the gravitational field strength; the elastic potential energy store of a stretched or compressed spring depends on its spring constant and extension (provided the spring is not inelastically deformed, i.e. it is not stretched past its limit of proportionality).
| Store | Equation | Units |
|---|---|---|
| Kinetic energy | Eₖ = ½ × m × v² | Eₖ in J, m in kg, v in m/s |
| Elastic potential energy | Eₑ = ½ × k × e² | Eₑ in J, k in N/m, e in m (only while the spring is not deformed inelastically) |
| Gravitational potential energy | Eₚ = m × g × h | Eₚ in J, m in kg, g in N/kg (9.8 N/kg on Earth), h in m |
⚠️ Common mistake: Forgetting to square the speed in the kinetic energy equation, or the extension in the elastic potential energy equation — doubling the speed of an object quadruples its kinetic energy, it does not just double it.
Energy changes in systems4.1.1.3
Definition: The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1 kg of the substance by 1°C (or 1 K).
Different substances need different amounts of energy to change temperature by the same amount, because they have different specific heat capacities — water has an unusually high specific heat capacity, which is why it takes a lot of energy to heat up (and a lot of energy to cool down).
| Equation | Units |
|---|---|
| ΔE = m × c × ΔT | ΔE in J, m in kg, c in J/kg°C, ΔT in °C |
- 1Measure the mass of the block (e.g. aluminium or copper) or liquid being heated, and record its starting temperature.
- 2Use an electric heater to supply a known amount of energy — measure the potential difference and current with a voltmeter and ammeter (or use a joulemeter) to calculate energy supplied = power × time.
- 3Record the temperature at regular intervals as the substance heats up, and find the temperature change ΔT for a known energy input.
- 4Use the equation ΔE = m × c × ΔT, rearranged to c = ΔE ÷ (m × ΔT), to calculate the specific heat capacity.
- 5Insulate the block or container to reduce energy losses to the surroundings, which would otherwise make the calculated specific heat capacity too high (since not all the electrical energy supplied went into raising the substance's temperature).
⚠️ Common mistake: Not accounting for energy losses to the surroundings during the specific heat capacity practical — insulating the sample and using a lid reduces (but does not remove) this source of error.
Power4.1.1.4
Definition: Power is the rate at which energy is transferred, or the rate at which work is done.
| Equation | Units |
|---|---|
| P = E ÷ t | P in W, E in J, t in s |
| P = W ÷ t | P in W, W (work done) in J, t in s |
- •An energy transfer of 1 joule per second is equal to a power of 1 watt.
- •A more powerful machine is not necessarily one that can do more work — it is one that can do the same amount of work in less time (or more work in the same time).
🧠 Remember: Power = energy ÷ time. A 3 kW kettle transfers energy three times as fast as a 1 kW kettle, not three times as much energy overall (that also depends on how long each is switched on for).
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